Problem: Solve for $x$ and $y$ using substitution. ${-x+2y = 8}$ ${y = -2x-11}$
Solution: Since $y$ has already been solved for, substitute $-2x-11$ for $y$ in the first equation. ${-x + 2}{(-2x-11)}{= 8}$ Simplify and solve for $x$ $-x-4x - 22 = 8$ $-5x-22 = 8$ $-5x-22{+22} = 8{+22}$ $-5x = 30$ $\dfrac{-5x}{{-5}} = \dfrac{30}{{-5}}$ ${x = -6}$ Now that you know ${x = -6}$ , plug it back into $\thinspace {y = -2x-11}\thinspace$ to find $y$ ${y = -2}{(-6)}{ - 11}$ $y = 12 - 11$ $y = 1$ You can also plug ${x = -6}$ into $\thinspace {-x+2y = 8}\thinspace$ and get the same answer for $y$ : ${-}{(-6)}{ + 2y = 8}$ ${y = 1}$